The vast majority of states have no excuse absentee voting and/or early in-person voting options. In addition, employees are legally required to allow time off to vote, though in the overwhelming majority of states, the early voting options make this unnecessary.
https://www.vote.org/early-voting-calendar/
If people want to participate, they have many options.
I've found that if you need to argue edge cases (single parent, hourly schedule that almost completely overlaps poll hours, no absentee, no early voting or mail-in, and an employer that violates law) as you have in your post, you do not have a compelling argument.